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Questions and Answers
If $\Delta ABC \cong \Delta DEF$, which of the following statements is true?
If $\Delta ABC \cong \Delta DEF$, which of the following statements is true?
- $\angle A \cong \angle D$, $\angle B \cong \angle E$, and $\angle C \cong \angle F$
- $AB \cong DE$, $BC \cong EF$, and $AC \cong DF$
- $AB \cong DE$, $AC \cong DF$, and $\angle A \cong \angle D$
- All of the above (correct)
In the given figure, if $\Delta ACT \cong \Delta SHE$, what is the value of $x$?
In the given figure, if $\Delta ACT \cong \Delta SHE$, what is the value of $x$?
- 40
- 50 (correct)
- 60
- 30
If $LM \cong ZR$, which congruence postulate can be used to prove that $\Delta NIM \cong \Delta ZER$?
If $LM \cong ZR$, which congruence postulate can be used to prove that $\Delta NIM \cong \Delta ZER$?
- Side-Angle-Side (SAS) Congruence Postulate
- Angle-Side-Angle (ASA) Congruence Postulate
- Side-Side-Side (SSS) Congruence Postulate (correct)
- Angle-Angle-Side (AAS) Congruence Postulate
If $\Delta ACT \cong \Delta SHE$, and $AC = 6$ cm, what is the length of $SH$?
If $\Delta ACT \cong \Delta SHE$, and $AC = 6$ cm, what is the length of $SH$?
Which of the following pairs of triangles appear to be congruent in the given figure?
Which of the following pairs of triangles appear to be congruent in the given figure?
Which theorem is best illustrated by two triangles that have two pairs of congruent corresponding sides and one pair of congruent corresponding angles?
Which theorem is best illustrated by two triangles that have two pairs of congruent corresponding sides and one pair of congruent corresponding angles?
If two triangles are congruent by the Side-Angle-Side (SAS) Congruence Theorem, what additional information is needed to prove congruence?
If two triangles are congruent by the Side-Angle-Side (SAS) Congruence Theorem, what additional information is needed to prove congruence?
Which congruence theorem can be used to prove two triangles are congruent if all three sides of one triangle are congruent to the corresponding sides of the other triangle?
Which congruence theorem can be used to prove two triangles are congruent if all three sides of one triangle are congruent to the corresponding sides of the other triangle?
If two triangles have two pairs of congruent corresponding angles and one pair of congruent corresponding sides, which congruence theorem can be used to prove the triangles are congruent?
If two triangles have two pairs of congruent corresponding angles and one pair of congruent corresponding sides, which congruence theorem can be used to prove the triangles are congruent?
If two triangles are congruent by the Side-Side-Side (SSS) Congruence Theorem, what additional information is needed to prove congruence?
If two triangles are congruent by the Side-Side-Side (SSS) Congruence Theorem, what additional information is needed to prove congruence?
Which of the following is NOT a valid congruence theorem for proving two triangles are congruent?
Which of the following is NOT a valid congruence theorem for proving two triangles are congruent?
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Study Notes
Congruent Triangles
- When assigning points on a truss, we need to identify pairs of triangles that appear to be congruent.
- Basis for choosing pairs of triangles: congruent triangles have the same shape and size.
Solving Corresponding Parts of Congruent Triangles
- When two triangles are congruent, their corresponding parts are equal.
- Example: ∆NIM and ∆ZER have 6 pairs of corresponding parts.
Practice Exercises
- Example 5: identify congruent triangles, write statement of correspondence, and find measures.
- Example 6: identify congruent triangles, write statement of correspondence, and find measures.
Geometry in Daily Life
- Geometry has numerous practical applications in daily life.
- Example: identifying objects around us that illustrate different theorems (e.g. congruent triangles).
Performance Task
- Take a picture of an object or cut pictures from a magazine/newspaper that illustrates a theorem.
- Identify which specific part corresponds to the theorem and mark the congruent parts.
- Specify the theorem illustrated on the picture.
- Each picture properly labeled with correct theorem will be given 10 points.
Illustrating Triangle Congruence
- Directions: identify vertices, angles, and sides of each triangle.
- Given ∆DRY ≅ ∆SOT, identify corresponding parts congruent to each given side or angle.
Illustrating Congruence Postulates
- SAS, ASA, and SSS congruence postulates can be used to prove triangle congruence.
- Identify additional corresponding parts needed to make triangles congruent using specified congruence postulates.
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